Circle A has a center at #(3 ,2 )# and an area of #13 pi#. Circle B has a center at #(9 ,6 )# and an area of #28 pi#. Do the circles overlap?

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Answer 1 · 2018-02-07T09:34:19

Circles Overlap

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In Circle A #pi R_A^2 = A_A = 13pi#

#R_A = sqrt((cancelpi * 13) / cancel(pi)) = sqrt13 #

Similarly in Circle B, #R_B = sqrt((cancel pi * 28)/cancel(pi)) = sqrt28 #

#R_A + R_B = sqrt13 + sqrt28 ~~ 8.8971#

Distance between the centers #O_A, O_B#

#vec(O_AO_B) = sqrt(9-6)^2 + (6-2)^2) = sqrt52 ~~ 7.2111#

Since #vec(O_AO_B) < R_A + R_B#, both the circles overlap.